269388
Four point size bodies each of mass \(M\) are fixed at four corners of a lightsqure frame of side length \(L\). The moment of inertia of the four bodies about an axis perpendicular to the plane of frame and passing through its centre is
1 \(4 \mathrm{ML}^{2}\)
2 \(2 \sqrt{2} \mathrm{ML}^{2}\)
3 \(2 \mathrm{ML}^{2}\)
4 \(\sqrt{2} M L^{2}\)
Explanation:
\(I=\sum m r^{2}\)
\(\mathrm{L} \quad\) Here \(r=\frac{L}{\sqrt{2}}\)
Rotational Motion
269389
Four particles each of mass '\(m\) ' are placed at the corners of a square of side length ' \(\ell\) '. The radius of gyration of the system about an axis perpendicular to the plane of square and passing through its centre is
1 \(\frac{\ell}{\sqrt{2}}\)
2 \(\frac{\ell}{2}\)
3 \(\ell\)
4 \(\sqrt{2} \ell\)
Explanation:
Radius of gyration \(k=\sqrt{\frac{I}{M}}=\sqrt{\frac{2 m l^{2}}{4 m}}=\frac{l}{\sqrt{2}}\)
Rotational Motion
269390
In the above problem the moment of inertia of four bodies about an axis perpendicular to the plane of frame and passing through a corner is
1 \(\mathrm{ML}^{2}\)
2 \(2 \mathrm{ML}^{2}\)
3 \(2 \sqrt{2} \mathrm{ML}^{2}\)
4 \(4 \mathrm{ML}^{2}\)
Explanation:
\(I=2 \boxminus M L^{2} \boxminus^{+M} \boxminus^{\sqrt{2}} \|^{;} ;=2 M L^{2}+2 M L^{2}=4 M L^{2}\)
Rotational Motion
269391
In above problem the moment of inertia of four bodies about an axis passing through opposite corners of frame is
269388
Four point size bodies each of mass \(M\) are fixed at four corners of a lightsqure frame of side length \(L\). The moment of inertia of the four bodies about an axis perpendicular to the plane of frame and passing through its centre is
1 \(4 \mathrm{ML}^{2}\)
2 \(2 \sqrt{2} \mathrm{ML}^{2}\)
3 \(2 \mathrm{ML}^{2}\)
4 \(\sqrt{2} M L^{2}\)
Explanation:
\(I=\sum m r^{2}\)
\(\mathrm{L} \quad\) Here \(r=\frac{L}{\sqrt{2}}\)
Rotational Motion
269389
Four particles each of mass '\(m\) ' are placed at the corners of a square of side length ' \(\ell\) '. The radius of gyration of the system about an axis perpendicular to the plane of square and passing through its centre is
1 \(\frac{\ell}{\sqrt{2}}\)
2 \(\frac{\ell}{2}\)
3 \(\ell\)
4 \(\sqrt{2} \ell\)
Explanation:
Radius of gyration \(k=\sqrt{\frac{I}{M}}=\sqrt{\frac{2 m l^{2}}{4 m}}=\frac{l}{\sqrt{2}}\)
Rotational Motion
269390
In the above problem the moment of inertia of four bodies about an axis perpendicular to the plane of frame and passing through a corner is
1 \(\mathrm{ML}^{2}\)
2 \(2 \mathrm{ML}^{2}\)
3 \(2 \sqrt{2} \mathrm{ML}^{2}\)
4 \(4 \mathrm{ML}^{2}\)
Explanation:
\(I=2 \boxminus M L^{2} \boxminus^{+M} \boxminus^{\sqrt{2}} \|^{;} ;=2 M L^{2}+2 M L^{2}=4 M L^{2}\)
Rotational Motion
269391
In above problem the moment of inertia of four bodies about an axis passing through opposite corners of frame is
269388
Four point size bodies each of mass \(M\) are fixed at four corners of a lightsqure frame of side length \(L\). The moment of inertia of the four bodies about an axis perpendicular to the plane of frame and passing through its centre is
1 \(4 \mathrm{ML}^{2}\)
2 \(2 \sqrt{2} \mathrm{ML}^{2}\)
3 \(2 \mathrm{ML}^{2}\)
4 \(\sqrt{2} M L^{2}\)
Explanation:
\(I=\sum m r^{2}\)
\(\mathrm{L} \quad\) Here \(r=\frac{L}{\sqrt{2}}\)
Rotational Motion
269389
Four particles each of mass '\(m\) ' are placed at the corners of a square of side length ' \(\ell\) '. The radius of gyration of the system about an axis perpendicular to the plane of square and passing through its centre is
1 \(\frac{\ell}{\sqrt{2}}\)
2 \(\frac{\ell}{2}\)
3 \(\ell\)
4 \(\sqrt{2} \ell\)
Explanation:
Radius of gyration \(k=\sqrt{\frac{I}{M}}=\sqrt{\frac{2 m l^{2}}{4 m}}=\frac{l}{\sqrt{2}}\)
Rotational Motion
269390
In the above problem the moment of inertia of four bodies about an axis perpendicular to the plane of frame and passing through a corner is
1 \(\mathrm{ML}^{2}\)
2 \(2 \mathrm{ML}^{2}\)
3 \(2 \sqrt{2} \mathrm{ML}^{2}\)
4 \(4 \mathrm{ML}^{2}\)
Explanation:
\(I=2 \boxminus M L^{2} \boxminus^{+M} \boxminus^{\sqrt{2}} \|^{;} ;=2 M L^{2}+2 M L^{2}=4 M L^{2}\)
Rotational Motion
269391
In above problem the moment of inertia of four bodies about an axis passing through opposite corners of frame is
269388
Four point size bodies each of mass \(M\) are fixed at four corners of a lightsqure frame of side length \(L\). The moment of inertia of the four bodies about an axis perpendicular to the plane of frame and passing through its centre is
1 \(4 \mathrm{ML}^{2}\)
2 \(2 \sqrt{2} \mathrm{ML}^{2}\)
3 \(2 \mathrm{ML}^{2}\)
4 \(\sqrt{2} M L^{2}\)
Explanation:
\(I=\sum m r^{2}\)
\(\mathrm{L} \quad\) Here \(r=\frac{L}{\sqrt{2}}\)
Rotational Motion
269389
Four particles each of mass '\(m\) ' are placed at the corners of a square of side length ' \(\ell\) '. The radius of gyration of the system about an axis perpendicular to the plane of square and passing through its centre is
1 \(\frac{\ell}{\sqrt{2}}\)
2 \(\frac{\ell}{2}\)
3 \(\ell\)
4 \(\sqrt{2} \ell\)
Explanation:
Radius of gyration \(k=\sqrt{\frac{I}{M}}=\sqrt{\frac{2 m l^{2}}{4 m}}=\frac{l}{\sqrt{2}}\)
Rotational Motion
269390
In the above problem the moment of inertia of four bodies about an axis perpendicular to the plane of frame and passing through a corner is
1 \(\mathrm{ML}^{2}\)
2 \(2 \mathrm{ML}^{2}\)
3 \(2 \sqrt{2} \mathrm{ML}^{2}\)
4 \(4 \mathrm{ML}^{2}\)
Explanation:
\(I=2 \boxminus M L^{2} \boxminus^{+M} \boxminus^{\sqrt{2}} \|^{;} ;=2 M L^{2}+2 M L^{2}=4 M L^{2}\)
Rotational Motion
269391
In above problem the moment of inertia of four bodies about an axis passing through opposite corners of frame is
